With the development of an adaptive filtering technology, many different adaptive filtering algorithms that can be applied to echo cancellation and noise cancellation emerge. The most common algorithm is a least mean square (LMS) algorithm, and implementation of the algorithm is relatively simple, but a convergence speed of an adaptive filter is relatively slow. To improve the convergence speed of the adaptive filter, a normalized least mean square (NLMS) algorithm is put forward, and an update step of the adaptive filter in this algorithm changes according to features of input signals. To further improve the convergence speed of the adaptive filter, an affine projection algorithm (APA) is further put forward, and a smaller projection order indicates lower calculation complexity, but a larger projection order indicates a faster convergence speed of the adaptive filter. The calculation complexity of the algorithm is higher than that of the LMS algorithm, but is lower than that of a least square (LS) algorithm.
Regardless of the NLMS algorithm or the APA algorithm, to enable a division operation or an inversion operation in a formula for determining a coefficient of the adaptive filter to have a solution, a stability factor of the adaptive filter is generally introduced. A value of the stability factor of the adaptive filter generally greatly affects the convergence speed of the adaptive filter and a steady state error after convergence. If the value of the stability factor of the adaptive filter is relatively large, the convergence speed of the adaptive filter is reduced, but the steady state error after convergence is smaller. If the value of the stability factor of the adaptive filter is relatively small, the convergence speed of the adaptive filter is faster, but the filter may diverge, or a problem that the steady state error becomes larger because the filter rejects to converge may occur.
However, in general, a constant is selected experientially as the value of the stability factor of the adaptive filter. As a result, the adaptive filter cannot reach a good balance between the convergence speed and steady state error performance.